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 A285574 Irregular triangle read by rows which arises from a diagram which is similar to the diagram of A261699, but here the even-indexed zig-zag lines are located on the right-hand side of the vertical axis of the diagram. 1
 1, 1, 1, 3, 1, 0, 1, 5, 1, 3, 0, 1, 0, 7, 1, 0, 0, 1, 3, 9, 1, 0, 5, 0, 1, 0, 0, 11, 1, 3, 0, 0, 1, 0, 0, 13, 1, 0, 7, 0, 1, 3, 5, 0, 15, 1, 0, 0, 0, 0, 1, 0, 0, 0, 17, 1, 3, 0, 9, 0, 1, 0, 0, 0, 19, 1, 0, 5, 0, 0, 1, 3, 0, 7, 0, 21, 1, 0, 0, 0, 11, 0, 1, 0, 0, 0, 0, 23, 1, 3, 0, 0, 0, 0, 1, 0, 5, 0, 0, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS In the diagram we have that: The number of horizontal line segments in the n-th row of the structure equals A001227(n), the number of partitions of n into consecutive parts. The number of horizontal line segments in the left-hand part of the n-th row equals A082647, the number of partitions of n into an odd number of consecutive parts. The number of horizontal line segments in the right-hand part of the n-th row equals A131576, the number of partitions of n into an even number of consecutive parts. The diagram explains the unusual ordering of the terms in the triangle A261699, in which the even-indexed zig-zag lines are located on the left-hand side of the vertical axis of the diagram. LINKS EXAMPLE Triangle begins: 1; 1; 1, 3; 1, 0, 1, 5; 1, 3, 0; 1, 0, 7; 1, 0, 0; 1, 3, 9; 1, 0, 5,  0; 1, 0, 0, 11; 1, 3, 0,  0; 1, 0, 0, 13; 1, 0, 7,  0; 1, 3, 5,  0, 15; 1, 0, 0,  0,  0; 1, 0, 0,  0, 17; 1, 3, 0,  9,  0; 1, 0, 0,  0, 19; 1, 0, 5,  0,  0; 1, 3, 0,  7,  0, 21; ... Illustration of initial terms of the diagram: Row                                           _ 1                                           _|1| 2                                         _|1  |_ 3                                       _|1    |3| 4                                     _|1      |0|_ 5                                   _|1       _|  5| 6                                 _|1        |3|  0|_ 7                               _|1          |0|    7| 8                             _|1           _|0|    0|_ 9                           _|1            |3  |_     9| 10                        _|1              |0  |5|    0|_ 11                      _|1               _|0  |0|     11| 12                    _|1                |3    |0|      0|_ 13                  _|1                  |0    |0|_      13| 14                _|1                   _|0   _|  7|      0|_ 15              _|1                    |3    |5|  0|       15| 16            _|1                      |0    |0|  0|        0|_ 17          _|1                       _|0    |0|  0|_        17| 18        _|1                        |3      |0|    9|        0|_ 19      _|1                          |0     _|0|    0|         19| 20    _|1                           _|0    |5  |_   0|          0|_ 21   |1                            |3      |0  |7|  0|           21| ... (Compare with the diagram of A261699.) CROSSREFS Positive terms give A182469. Row n has length A003056(n). The sum of row n is A000593(n). Column k starts in row A000217(k). The number of positive terms in row n is A001227(n). Cf. A082647, A131576, A196020, A235791, A236104, A237048, A237591, A237593, A245092, A259176, A259177, A261699, A279820. Sequence in context: A050143 A103495 A261699 * A081719 A327618 A121314 Adjacent sequences:  A285571 A285572 A285573 * A285575 A285576 A285577 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Apr 21 2017 STATUS approved

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Last modified June 18 19:47 EDT 2021. Contains 345120 sequences. (Running on oeis4.)